Estimation of Random Channel Gain for SISO Visible Light Communications System

Abstract

In this article, the estimation of random channel gain is studied for a single-input single-output (SISO) visible light communication (VLC) system. Five different estimators, namely maximum likelihood (ML), least square (LS), maximum posteriori probability (MAP), linear minimum mean square error (LMMSE), and minimum mean square error (MMSE), are proposed. The performances of these estimators are compared with the derived Bayesian Cramér–Rao lower bound (BCRLB), which can be used as a benchmark to evaluate the efficiency of the unbiased estimators. The presented analytical results, corroborated with Monte Carlo simulations, indicate that the MMSE estimator provides the best results. Additionally, the increasing number of pilot symbols as well as the ascending transmitted power improve the system performance. On the other hand, the noise variance has a negative effect on the channel estimation in terms of mean square error (MSE), and thus, it can dramatically reduce the performance of the estimators.